Abstract

Separation Logic is a recent development in programming logic which has been applied by Peter O’Hearn to concurrency based on critical sections as well as semaphores. In this work, we go one step further and apply it to fine-grained concurrency. We note that O’Hearn’s formulation of Concurrent Separation Logic is by and large applicable to fine-grained concurrent programs with only minor adaptations. However, proving substantial properties of such programs involves the employment of sophisticated ``permissions’’ frameworks so that different processes can have different levels of access and exchange such access.

We illustrate these techniques by showing the correctness proof of a concurrent garbage collector originally studied by Dijkstra et al. The original proof is based on informal reasoning, and it is said to have been very challenging to ensure its validity. Our techniques formalise this proof, but we find that there are significant details that need to be filled in.